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A124987
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Primes of the form 12k+5 generated recursively. Initial prime is 5. General term is a(n) = Min {p is prime; p divides 4+Q^2; p == 5 (mod 12)}, where Q is the product of previous terms in the sequence.
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1
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5, 29, 17, 6076229, 1289, 78067083126343039013, 521, 8606045503613, 15837917, 1873731749, 809, 137, 2237, 17729
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OFFSET
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1,1
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COMMENTS
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Since Q is odd, all prime divisors of 4+Q^2 are congruent to 1 modulo 4.
At least one prime divisor of 4+Q^2 is congruent to 2 modulo 3 and hence to 5 modulo 12.
The first two terms are the same as those of A057208.
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LINKS
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EXAMPLE
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a(3) = 17 is the smallest prime divisor congruent to 5 mod 12 of 4+Q^2 = 21029 = 17 * 1237, where Q = 5 * 29.
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MATHEMATICA
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a={5}; q=1;
For[n=2, n<=5, n++,
q=q*Last[a];
AppendTo[a, Min[Select[FactorInteger[q^2+4][[All, 1]], Mod[#, 12]==5 &]]];
];
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CROSSREFS
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KEYWORD
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more,nonn
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AUTHOR
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STATUS
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approved
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